I'm not sure this is correct but this is how I understand it. When playing back a recorded stereo music source the two tracks left and right don't always differ. So with joint stereo the MP3 compressor deletes the left track or combines the left and right track in times when the two do not differ and retain both left and right when they do differ. This is very much like the way VBR (Variable Bit Rate) works.
It is used to aid in reducing the overall size of the MP3 file.
In theory it does not lessen the overall quality of the music. I say in theory beecause it has the potential for flaws as with any compression method.